Find 𝑥 to two decimal places.
What do we notice about this image? First of all, we notice that it’s a right triangle. Because it’s a right triangle, we can use our trig ratios. Side length 𝑥 is opposite the angle we’re given and side length 12 is adjacent to the angle we’re given.
Opposite over adjacent side lengths tell us that we’re dealing with the tangent ratio. Tangent of 20 degrees is equal to the opposite side length 𝑥 over the adjacent side length 12. Tangent of 20 degrees equals 𝑥 over 12.
We’re solving for 𝑥. So we multiply the right side of our equation by 12. If we multiply the right side, we have to multiply the left side. 12 times the tangent of 20 degrees is equal the side length 𝑥. Using a calculator, we calculate the tangent of 20 degrees and then multiply that by 12. It gives us a decimal number that doesn’t terminate.
We want to round this number to two decimal places. In the second decimal place, there is a six. We look to the right of that and we have a seven, which is greater than five. Our six in the hundredths place is rounded up to a seven. And everything to the left of the hundredths place stays the same.
Side length 𝑥 is equal to 4.37.